Students at HT are planning to invest $1 million in a rock concert to be held 1 year from now. The students figure that they will obtain $3 million revenue from their $1 million investment - unless, my goodness, it rains. If it rains, they will lose their entire investment.

There is a 50% chance that it will rain the day of the concert. The faculty suggests that they buy rain insurance. The students can buy one unit of insurance for $0.50, and this unit pays $1 if it rains and nothing if it does not. They may purchase as many units as they wish, up to $3 million.

a) What is the expected rate of return on their investment if they buy u units of insurance?

b) What number of units will minimize the standard deviation of their return? What is this minimum value? And what is the corresponding return?